9,249 research outputs found
Combined Effect of QCD Resummation and QED Radiative Correction to W boson Observables at the Tevatron
A precise determination of the W boson mass at the Fermilab Tevatron requires
a theoretical calculation in which the effects of the initial-state multiple
soft-gluon emission and the final-state photonic correction are simultaneously
included . Here, we present such a calculation and discuss its prediction on
the transverse mass distribution of the W boson and the transverse momentum
distribution of its decay charged lepton, which are the most relevant
observables for measuring the W boson mass at hadron colliders.Comment: 10 pages, 3 Postscript figures, uses revtex4.st
On the Convergence of Decentralized Gradient Descent
Consider the consensus problem of minimizing where
each is only known to one individual agent out of a connected network
of agents. All the agents shall collaboratively solve this problem and
obtain the solution subject to data exchanges restricted to between neighboring
agents. Such algorithms avoid the need of a fusion center, offer better network
load balance, and improve data privacy. We study the decentralized gradient
descent method in which each agent updates its variable , which is
a local approximate to the unknown variable , by combining the average of
its neighbors' with the negative gradient step .
The iteration is where the averaging coefficients form a symmetric doubly stochastic matrix
. We analyze the convergence of this
iteration and derive its converge rate, assuming that each is proper
closed convex and lower bounded, is Lipschitz continuous with
constant , and stepsize is fixed. Provided that where , the objective error at the averaged
solution, , reduces at a speed of
until it reaches . If are further (restricted) strongly
convex, then both and each converge
to the global minimizer at a linear rate until reaching an
-neighborhood of . We also develop an iteration for
decentralized basis pursuit and establish its linear convergence to an
-neighborhood of the true unknown sparse signal
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